Algebra - Mixed Practice (Up to Radical Expressions)

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Algebra - Mixed Practice (Up to Radical Expressions)

This section has three worksheets. The first two include simplifying radical expressions and the third includes solving radical equations.

In the first worksheet, all radical expressions have radicals only in the numerator. In the second worksheet, there will also be radicals in the denominator, and are simplified by multiplying numerator and denominator by the conjugate of the denominator.

In the final worksheet, most of the problems involve squaring each side just once. The final three problems require squaring twice.

Worksheet 9.1

Writing algebraic expressions
Solving linear equations
Simplifying radical expressions

Worksheet 9.2

Simplifying complex fractions
Multiplying difference of squares
Simplifying radical expressions

Worksheet 9.3

Squaring binomials
Writing and simplifying radical expressions
Solving radical equations

Worksheet Sets in this Series

Worksheets for this section are below the index. Click the "Overview" link to get a more detailed view of the entire series.

Lesson by Mr. Twitchell

Handouts/Worksheets

Mixed Practice 9.1

Write algebraic expressions

The sum of a number and its square root
The square root of five less than twice a number
A third of the square root of a number
Two more than a number, times the square root of seven less than the number
The product of half a number with the square root of ten times the sum of seven and the number squared

Solve the following linear equations
3x + 20 = 12
2(x - 5) = 24
3x + 2(-x + 5) = 30
2x(x + 7) = x(2x - 10) + 4(x + 2)
(5x + 1) - (4x - 1) + (3x + 1) - (2x - 1) + (x + 1) = 18

Simplify the radical expressions
96
240
98
32
+
128
10
90
+ 5
810
3
+
5
+
27
+
45
2
3
54
-
1
2
24
10
(
40
-
10
+
90
)
3
2
(
2
+
3
+
8
)
14 + 10
14 - 10

Mixed Practice 9.1: Answer Key

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Mixed Practice 9.2

Simplify the following expressions

a²
b
c
b
x + 2
2x + 4
2x
x + 1
x - 1
x² - 1
x - 1
1 +
1
x
1 -
1
x
(x - 2)(x + 2) =
(3x - 4)(3x + 4) =
(
1
2
x +
y
3
)(
1
2
x -
y
3
) =
(2 +
2
)(2 -
2
) =
(5 -
3
)(5 +
3
) =
(7 + 3
5
)(7 - 3
5
) =
5
2
=
3
3 -
3
=
1 +
2
1 -
2
=
10
7
-
2
=
1 +
3
12
+ 1

Mixed Practice 9.2: Answer Key

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Mixed Practice 9.3

Simplify the following expressions

(x + 3)² =
(x - 5)² =
(2x - 3)² =
(x +
3
)² =
(
3
-
2
)² =
The product of one less than the square root of a number with one more than the square root of that number
The square of the sum of one and the square root of a number
Half of a number times the square root of 4 less than four times the number
Seven divided by the difference between the square root of ten and the square root of three
The reciprocal of three more than the square root of seven

Solve the following radical equations
x
= 2
7
5 +
x
= 10
x
= x - 6
x - 1
=
4x - 13
3
x
- 1
=
1
3
x
+
x - 5
= 5
x - 6
-
x + 7
= -1
6 -
x
=
x - 12

Mixed Practice 9.3: Answer Key

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